1 /*
2  * OpenSimplex (Simplectic) Noise in Java.
3  * by Kurt Spencer
4  *
5  * v1.1 (October 5, 2014)
6  * - Added 2D and 4D implementations.
7  * - Proper gradient sets for all dimensions, from a
8  *   dimensionally-generalizable scheme with an actual
9  *   rhyme and reason behind it.
10  * - Removed default permutation array in favor of
11  *   default seed.
12  * - Changed seed-based constructor to be independent
13  *   of any particular randomization library, so results
14  *   will be the same when ported to other languages.
15  */
16 
17 /**
18  * Ported to D by Brian Schott
19  */
20 
21 module opensimplexnoise;
22 import std.traits;
23 
24 public class OpenSimplexNoise(T) if (isFloatingPoint!T) {
25 
26 	enum T STRETCH_CONSTANT_2D = -0.211324865405187;    //(1/Math.sqrt(2+1)-1)/2;
27 	enum T SQUISH_CONSTANT_2D = 0.366025403784439;      //(Math.sqrt(2+1)-1)/2;
28 	enum T STRETCH_CONSTANT_3D = -1.0 / 6;              //(1/Math.sqrt(3+1)-1)/3;
29 	enum T SQUISH_CONSTANT_3D = 1.0 / 3;                //(Math.sqrt(3+1)-1)/3;
30 	enum T STRETCH_CONSTANT_4D = -0.138196601125011;    //(1/Math.sqrt(4+1)-1)/4;
31 	enum T SQUISH_CONSTANT_4D = 0.309016994374947;      //(Math.sqrt(4+1)-1)/4;
32 
33 	enum T NORM_CONSTANT_2D = 47;
34 	enum T NORM_CONSTANT_3D = 103;
35 	enum T NORM_CONSTANT_4D = 30;
36 
37 	enum long DEFAULT_SEED = 0;
38 
39 	private short[] perm;
40 	private short[] permGradIndex3D;
41 
42 	public this() {
43 		this(DEFAULT_SEED);
44 	}
45 
46 	public this(short[] perm) {
47 		this.perm = perm;
48 		permGradIndex3D = new short[256];
49 
50 		for (int i = 0; i < 256; i++) {
51 			//Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array.
52 			permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3);
53 		}
54 	}
55 
56 	//Initializes the class using a permutation array generated from a 64-bit seed.
57 	//Generates a proper permutation (i.e. doesn't merely perform N successive pair swaps on a base array)
58 	//Uses a simple 64-bit LCG.
59 	public this(long seed) {
60 		perm = new short[256];
61 		permGradIndex3D = new short[256];
62 		short[] source = new short[256];
63 		for (short i = 0; i < 256; i++)
64 			source[i] = i;
65 		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
66 		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
67 		seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
68 		for (int i = 255; i >= 0; i--) {
69 			seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L;
70 			int r = cast(int)((seed + 31) % (i + 1));
71 			if (r < 0)
72 				r += (i + 1);
73 			perm[i] = source[r];
74 			permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3);
75 			source[r] = source[i];
76 		}
77 	}
78 
79 	//2D OpenSimplex (Simplectic) Noise.
80 	public T eval(T x, T y) {
81 
82 		//Place input coordinates onto grid.
83 		T stretchOffset = (x + y) * STRETCH_CONSTANT_2D;
84 		T xs = x + stretchOffset;
85 		T ys = y + stretchOffset;
86 
87 		//Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
88 		int xsb = fastFloor(xs);
89 		int ysb = fastFloor(ys);
90 
91 		//Skew out to get actual coordinates of rhombus origin. We'll need these later.
92 		T squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D;
93 		T xb = xsb + squishOffset;
94 		T yb = ysb + squishOffset;
95 
96 		//Compute grid coordinates relative to rhombus origin.
97 		T xins = xs - xsb;
98 		T yins = ys - ysb;
99 
100 		//Sum those together to get a value that determines which region we're in.
101 		T inSum = xins + yins;
102 
103 		//Positions relative to origin point.
104 		T dx0 = x - xb;
105 		T dy0 = y - yb;
106 
107 		//We'll be defining these inside the next block and using them afterwards.
108 		T dx_ext, dy_ext;
109 		int xsv_ext, ysv_ext;
110 
111 		T value = 0;
112 
113 		//Contribution (1,0)
114 		T dx1 = dx0 - 1 - SQUISH_CONSTANT_2D;
115 		T dy1 = dy0 - 0 - SQUISH_CONSTANT_2D;
116 		T attn1 = 2 - dx1 * dx1 - dy1 * dy1;
117 		if (attn1 > 0) {
118 			attn1 *= attn1;
119 			value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1);
120 		}
121 
122 		//Contribution (0,1)
123 		T dx2 = dx0 - 0 - SQUISH_CONSTANT_2D;
124 		T dy2 = dy0 - 1 - SQUISH_CONSTANT_2D;
125 		T attn2 = 2 - dx2 * dx2 - dy2 * dy2;
126 		if (attn2 > 0) {
127 			attn2 *= attn2;
128 			value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2);
129 		}
130 
131 		if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0)
132 			T zins = 1 - inSum;
133 			if (zins > xins || zins > yins) { //(0,0) is one of the closest two triangular vertices
134 				if (xins > yins) {
135 					xsv_ext = xsb + 1;
136 					ysv_ext = ysb - 1;
137 					dx_ext = dx0 - 1;
138 					dy_ext = dy0 + 1;
139 				} else {
140 					xsv_ext = xsb - 1;
141 					ysv_ext = ysb + 1;
142 					dx_ext = dx0 + 1;
143 					dy_ext = dy0 - 1;
144 				}
145 			} else { //(1,0) and (0,1) are the closest two vertices.
146 				xsv_ext = xsb + 1;
147 				ysv_ext = ysb + 1;
148 				dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
149 				dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
150 			}
151 		} else { //We're inside the triangle (2-Simplex) at (1,1)
152 			T zins = 2 - inSum;
153 			if (zins < xins || zins < yins) { //(0,0) is one of the closest two triangular vertices
154 				if (xins > yins) {
155 					xsv_ext = xsb + 2;
156 					ysv_ext = ysb + 0;
157 					dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D;
158 					dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D;
159 				} else {
160 					xsv_ext = xsb + 0;
161 					ysv_ext = ysb + 2;
162 					dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D;
163 					dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D;
164 				}
165 			} else { //(1,0) and (0,1) are the closest two vertices.
166 				dx_ext = dx0;
167 				dy_ext = dy0;
168 				xsv_ext = xsb;
169 				ysv_ext = ysb;
170 			}
171 			xsb += 1;
172 			ysb += 1;
173 			dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D;
174 			dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D;
175 		}
176 
177 		//Contribution (0,0) or (1,1)
178 		T attn0 = 2 - dx0 * dx0 - dy0 * dy0;
179 		if (attn0 > 0) {
180 			attn0 *= attn0;
181 			value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0);
182 		}
183 
184 		//Extra Vertex
185 		T attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
186 		if (attn_ext > 0) {
187 			attn_ext *= attn_ext;
188 			value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext);
189 		}
190 
191 		return value / NORM_CONSTANT_2D;
192 	}
193 
194 	//3D OpenSimplex (Simplectic) Noise.
195 	public T eval(T x, T y, T z) {
196 
197 		//Place input coordinates on simplectic honeycomb.
198 		T stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D;
199 		T xs = x + stretchOffset;
200 		T ys = y + stretchOffset;
201 		T zs = z + stretchOffset;
202 
203 		//Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
204 		int xsb = fastFloor(xs);
205 		int ysb = fastFloor(ys);
206 		int zsb = fastFloor(zs);
207 
208 		//Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
209 		T squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D;
210 		T xb = xsb + squishOffset;
211 		T yb = ysb + squishOffset;
212 		T zb = zsb + squishOffset;
213 
214 		//Compute simplectic honeycomb coordinates relative to rhombohedral origin.
215 		T xins = xs - xsb;
216 		T yins = ys - ysb;
217 		T zins = zs - zsb;
218 
219 		//Sum those together to get a value that determines which region we're in.
220 		T inSum = xins + yins + zins;
221 
222 		//Positions relative to origin point.
223 		T dx0 = x - xb;
224 		T dy0 = y - yb;
225 		T dz0 = z - zb;
226 
227 		//We'll be defining these inside the next block and using them afterwards.
228 		T dx_ext0, dy_ext0, dz_ext0;
229 		T dx_ext1, dy_ext1, dz_ext1;
230 		int xsv_ext0, ysv_ext0, zsv_ext0;
231 		int xsv_ext1, ysv_ext1, zsv_ext1;
232 
233 		T value = 0;
234 		if (inSum <= 1) { //We're inside the tetrahedron (3-Simplex) at (0,0,0)
235 
236 			//Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest.
237 			byte aPoint = 0x01;
238 			T aScore = xins;
239 			byte bPoint = 0x02;
240 			T bScore = yins;
241 			if (aScore >= bScore && zins > bScore) {
242 				bScore = zins;
243 				bPoint = 0x04;
244 			} else if (aScore < bScore && zins > aScore) {
245 				aScore = zins;
246 				aPoint = 0x04;
247 			}
248 
249 			//Now we determine the two lattice points not part of the tetrahedron that may contribute.
250 			//This depends on the closest two tetrahedral vertices, including (0,0,0)
251 			T wins = 1 - inSum;
252 			if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices.
253 				byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
254 
255 				if ((c & 0x01) == 0) {
256 					xsv_ext0 = xsb - 1;
257 					xsv_ext1 = xsb;
258 					dx_ext0 = dx0 + 1;
259 					dx_ext1 = dx0;
260 				} else {
261 					xsv_ext0 = xsv_ext1 = xsb + 1;
262 					dx_ext0 = dx_ext1 = dx0 - 1;
263 				}
264 
265 				if ((c & 0x02) == 0) {
266 					ysv_ext0 = ysv_ext1 = ysb;
267 					dy_ext0 = dy_ext1 = dy0;
268 					if ((c & 0x01) == 0) {
269 						ysv_ext1 -= 1;
270 						dy_ext1 += 1;
271 					} else {
272 						ysv_ext0 -= 1;
273 						dy_ext0 += 1;
274 					}
275 				} else {
276 					ysv_ext0 = ysv_ext1 = ysb + 1;
277 					dy_ext0 = dy_ext1 = dy0 - 1;
278 				}
279 
280 				if ((c & 0x04) == 0) {
281 					zsv_ext0 = zsb;
282 					zsv_ext1 = zsb - 1;
283 					dz_ext0 = dz0;
284 					dz_ext1 = dz0 + 1;
285 				} else {
286 					zsv_ext0 = zsv_ext1 = zsb + 1;
287 					dz_ext0 = dz_ext1 = dz0 - 1;
288 				}
289 			} else { //(0,0,0) is not one of the closest two tetrahedral vertices.
290 				byte c = cast(byte)(aPoint | bPoint); //Our two extra vertices are determined by the closest two.
291 
292 				if ((c & 0x01) == 0) {
293 					xsv_ext0 = xsb;
294 					xsv_ext1 = xsb - 1;
295 					dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D;
296 					dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D;
297 				} else {
298 					xsv_ext0 = xsv_ext1 = xsb + 1;
299 					dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
300 					dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
301 				}
302 
303 				if ((c & 0x02) == 0) {
304 					ysv_ext0 = ysb;
305 					ysv_ext1 = ysb - 1;
306 					dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D;
307 					dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D;
308 				} else {
309 					ysv_ext0 = ysv_ext1 = ysb + 1;
310 					dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
311 					dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
312 				}
313 
314 				if ((c & 0x04) == 0) {
315 					zsv_ext0 = zsb;
316 					zsv_ext1 = zsb - 1;
317 					dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D;
318 					dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D;
319 				} else {
320 					zsv_ext0 = zsv_ext1 = zsb + 1;
321 					dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
322 					dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
323 				}
324 			}
325 
326 			//Contribution (0,0,0)
327 			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
328 			if (attn0 > 0) {
329 				attn0 *= attn0;
330 				value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0);
331 			}
332 
333 			//Contribution (1,0,0)
334 			T dx1 = dx0 - 1 - SQUISH_CONSTANT_3D;
335 			T dy1 = dy0 - 0 - SQUISH_CONSTANT_3D;
336 			T dz1 = dz0 - 0 - SQUISH_CONSTANT_3D;
337 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
338 			if (attn1 > 0) {
339 				attn1 *= attn1;
340 				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
341 			}
342 
343 			//Contribution (0,1,0)
344 			T dx2 = dx0 - 0 - SQUISH_CONSTANT_3D;
345 			T dy2 = dy0 - 1 - SQUISH_CONSTANT_3D;
346 			T dz2 = dz1;
347 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
348 			if (attn2 > 0) {
349 				attn2 *= attn2;
350 				value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
351 			}
352 
353 			//Contribution (0,0,1)
354 			T dx3 = dx2;
355 			T dy3 = dy1;
356 			T dz3 = dz0 - 1 - SQUISH_CONSTANT_3D;
357 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
358 			if (attn3 > 0) {
359 				attn3 *= attn3;
360 				value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
361 			}
362 		} else if (inSum >= 2) { //We're inside the tetrahedron (3-Simplex) at (1,1,1)
363 
364 			//Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1).
365 			byte aPoint = 0x06;
366 			T aScore = xins;
367 			byte bPoint = 0x05;
368 			T bScore = yins;
369 			if (aScore <= bScore && zins < bScore) {
370 				bScore = zins;
371 				bPoint = 0x03;
372 			} else if (aScore > bScore && zins < aScore) {
373 				aScore = zins;
374 				aPoint = 0x03;
375 			}
376 
377 			//Now we determine the two lattice points not part of the tetrahedron that may contribute.
378 			//This depends on the closest two tetrahedral vertices, including (1,1,1)
379 			T wins = 3 - inSum;
380 			if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices.
381 				byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
382 
383 				if ((c & 0x01) != 0) {
384 					xsv_ext0 = xsb + 2;
385 					xsv_ext1 = xsb + 1;
386 					dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D;
387 					dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
388 				} else {
389 					xsv_ext0 = xsv_ext1 = xsb;
390 					dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D;
391 				}
392 
393 				if ((c & 0x02) != 0) {
394 					ysv_ext0 = ysv_ext1 = ysb + 1;
395 					dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
396 					if ((c & 0x01) != 0) {
397 						ysv_ext1 += 1;
398 						dy_ext1 -= 1;
399 					} else {
400 						ysv_ext0 += 1;
401 						dy_ext0 -= 1;
402 					}
403 				} else {
404 					ysv_ext0 = ysv_ext1 = ysb;
405 					dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D;
406 				}
407 
408 				if ((c & 0x04) != 0) {
409 					zsv_ext0 = zsb + 1;
410 					zsv_ext1 = zsb + 2;
411 					dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
412 					dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D;
413 				} else {
414 					zsv_ext0 = zsv_ext1 = zsb;
415 					dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D;
416 				}
417 			} else { //(1,1,1) is not one of the closest two tetrahedral vertices.
418 				byte c = cast(byte)(aPoint & bPoint); //Our two extra vertices are determined by the closest two.
419 
420 				if ((c & 0x01) != 0) {
421 					xsv_ext0 = xsb + 1;
422 					xsv_ext1 = xsb + 2;
423 					dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
424 					dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D;
425 				} else {
426 					xsv_ext0 = xsv_ext1 = xsb;
427 					dx_ext0 = dx0 - SQUISH_CONSTANT_3D;
428 					dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
429 				}
430 
431 				if ((c & 0x02) != 0) {
432 					ysv_ext0 = ysb + 1;
433 					ysv_ext1 = ysb + 2;
434 					dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
435 					dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D;
436 				} else {
437 					ysv_ext0 = ysv_ext1 = ysb;
438 					dy_ext0 = dy0 - SQUISH_CONSTANT_3D;
439 					dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
440 				}
441 
442 				if ((c & 0x04) != 0) {
443 					zsv_ext0 = zsb + 1;
444 					zsv_ext1 = zsb + 2;
445 					dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
446 					dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D;
447 				} else {
448 					zsv_ext0 = zsv_ext1 = zsb;
449 					dz_ext0 = dz0 - SQUISH_CONSTANT_3D;
450 					dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
451 				}
452 			}
453 
454 			//Contribution (1,1,0)
455 			T dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
456 			T dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
457 			T dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D;
458 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
459 			if (attn3 > 0) {
460 				attn3 *= attn3;
461 				value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3);
462 			}
463 
464 			//Contribution (1,0,1)
465 			T dx2 = dx3;
466 			T dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D;
467 			T dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
468 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
469 			if (attn2 > 0) {
470 				attn2 *= attn2;
471 				value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2);
472 			}
473 
474 			//Contribution (0,1,1)
475 			T dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D;
476 			T dy1 = dy3;
477 			T dz1 = dz2;
478 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
479 			if (attn1 > 0) {
480 				attn1 *= attn1;
481 				value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1);
482 			}
483 
484 			//Contribution (1,1,1)
485 			dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
486 			dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
487 			dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
488 			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
489 			if (attn0 > 0) {
490 				attn0 *= attn0;
491 				value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
492 			}
493 		} else { //We're inside the octahedron (Rectified 3-Simplex) in between.
494 			T aScore;
495 			byte aPoint;
496 			bool aIsFurtherSide;
497 			T bScore;
498 			byte bPoint;
499 			bool bIsFurtherSide;
500 
501 			//Decide between point (0,0,1) and (1,1,0) as closest
502 			T p1 = xins + yins;
503 			if (p1 > 1) {
504 				aScore = p1 - 1;
505 				aPoint = 0x03;
506 				aIsFurtherSide = true;
507 			} else {
508 				aScore = 1 - p1;
509 				aPoint = 0x04;
510 				aIsFurtherSide = false;
511 			}
512 
513 			//Decide between point (0,1,0) and (1,0,1) as closest
514 			T p2 = xins + zins;
515 			if (p2 > 1) {
516 				bScore = p2 - 1;
517 				bPoint = 0x05;
518 				bIsFurtherSide = true;
519 			} else {
520 				bScore = 1 - p2;
521 				bPoint = 0x02;
522 				bIsFurtherSide = false;
523 			}
524 
525 			//The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer.
526 			T p3 = yins + zins;
527 			if (p3 > 1) {
528 				T score = p3 - 1;
529 				if (aScore <= bScore && aScore < score) {
530 					aScore = score;
531 					aPoint = 0x06;
532 					aIsFurtherSide = true;
533 				} else if (aScore > bScore && bScore < score) {
534 					bScore = score;
535 					bPoint = 0x06;
536 					bIsFurtherSide = true;
537 				}
538 			} else {
539 				T score = 1 - p3;
540 				if (aScore <= bScore && aScore < score) {
541 					aScore = score;
542 					aPoint = 0x01;
543 					aIsFurtherSide = false;
544 				} else if (aScore > bScore && bScore < score) {
545 					bScore = score;
546 					bPoint = 0x01;
547 					bIsFurtherSide = false;
548 				}
549 			}
550 
551 			//Where each of the two closest points are determines how the extra two vertices are calculated.
552 			if (aIsFurtherSide == bIsFurtherSide) {
553 				if (aIsFurtherSide) { //Both closest points on (1,1,1) side
554 
555 					//One of the two extra points is (1,1,1)
556 					dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D;
557 					dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D;
558 					dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D;
559 					xsv_ext0 = xsb + 1;
560 					ysv_ext0 = ysb + 1;
561 					zsv_ext0 = zsb + 1;
562 
563 					//Other extra point is based on the shared axis.
564 					byte c = cast(byte)(aPoint & bPoint);
565 					if ((c & 0x01) != 0) {
566 						dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D;
567 						dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
568 						dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
569 						xsv_ext1 = xsb + 2;
570 						ysv_ext1 = ysb;
571 						zsv_ext1 = zsb;
572 					} else if ((c & 0x02) != 0) {
573 						dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
574 						dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D;
575 						dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
576 						xsv_ext1 = xsb;
577 						ysv_ext1 = ysb + 2;
578 						zsv_ext1 = zsb;
579 					} else {
580 						dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
581 						dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
582 						dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D;
583 						xsv_ext1 = xsb;
584 						ysv_ext1 = ysb;
585 						zsv_ext1 = zsb + 2;
586 					}
587 				} else {//Both closest points on (0,0,0) side
588 
589 					//One of the two extra points is (0,0,0)
590 					dx_ext0 = dx0;
591 					dy_ext0 = dy0;
592 					dz_ext0 = dz0;
593 					xsv_ext0 = xsb;
594 					ysv_ext0 = ysb;
595 					zsv_ext0 = zsb;
596 
597 					//Other extra point is based on the omitted axis.
598 					byte c = cast(byte)(aPoint | bPoint);
599 					if ((c & 0x01) == 0) {
600 						dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D;
601 						dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
602 						dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
603 						xsv_ext1 = xsb - 1;
604 						ysv_ext1 = ysb + 1;
605 						zsv_ext1 = zsb + 1;
606 					} else if ((c & 0x02) == 0) {
607 						dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
608 						dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D;
609 						dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D;
610 						xsv_ext1 = xsb + 1;
611 						ysv_ext1 = ysb - 1;
612 						zsv_ext1 = zsb + 1;
613 					} else {
614 						dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D;
615 						dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D;
616 						dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D;
617 						xsv_ext1 = xsb + 1;
618 						ysv_ext1 = ysb + 1;
619 						zsv_ext1 = zsb - 1;
620 					}
621 				}
622 			} else { //One point on (0,0,0) side, one point on (1,1,1) side
623 				byte c1, c2;
624 				if (aIsFurtherSide) {
625 					c1 = aPoint;
626 					c2 = bPoint;
627 				} else {
628 					c1 = bPoint;
629 					c2 = aPoint;
630 				}
631 
632 				//One contribution is a permutation of (1,1,-1)
633 				if ((c1 & 0x01) == 0) {
634 					dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D;
635 					dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
636 					dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
637 					xsv_ext0 = xsb - 1;
638 					ysv_ext0 = ysb + 1;
639 					zsv_ext0 = zsb + 1;
640 				} else if ((c1 & 0x02) == 0) {
641 					dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
642 					dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D;
643 					dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D;
644 					xsv_ext0 = xsb + 1;
645 					ysv_ext0 = ysb - 1;
646 					zsv_ext0 = zsb + 1;
647 				} else {
648 					dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D;
649 					dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D;
650 					dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D;
651 					xsv_ext0 = xsb + 1;
652 					ysv_ext0 = ysb + 1;
653 					zsv_ext0 = zsb - 1;
654 				}
655 
656 				//One contribution is a permutation of (0,0,2)
657 				dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D;
658 				dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D;
659 				dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D;
660 				xsv_ext1 = xsb;
661 				ysv_ext1 = ysb;
662 				zsv_ext1 = zsb;
663 				if ((c2 & 0x01) != 0) {
664 					dx_ext1 -= 2;
665 					xsv_ext1 += 2;
666 				} else if ((c2 & 0x02) != 0) {
667 					dy_ext1 -= 2;
668 					ysv_ext1 += 2;
669 				} else {
670 					dz_ext1 -= 2;
671 					zsv_ext1 += 2;
672 				}
673 			}
674 
675 			//Contribution (1,0,0)
676 			T dx1 = dx0 - 1 - SQUISH_CONSTANT_3D;
677 			T dy1 = dy0 - 0 - SQUISH_CONSTANT_3D;
678 			T dz1 = dz0 - 0 - SQUISH_CONSTANT_3D;
679 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
680 			if (attn1 > 0) {
681 				attn1 *= attn1;
682 				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1);
683 			}
684 
685 			//Contribution (0,1,0)
686 			T dx2 = dx0 - 0 - SQUISH_CONSTANT_3D;
687 			T dy2 = dy0 - 1 - SQUISH_CONSTANT_3D;
688 			T dz2 = dz1;
689 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
690 			if (attn2 > 0) {
691 				attn2 *= attn2;
692 				value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2);
693 			}
694 
695 			//Contribution (0,0,1)
696 			T dx3 = dx2;
697 			T dy3 = dy1;
698 			T dz3 = dz0 - 1 - SQUISH_CONSTANT_3D;
699 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
700 			if (attn3 > 0) {
701 				attn3 *= attn3;
702 				value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3);
703 			}
704 
705 			//Contribution (1,1,0)
706 			T dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D;
707 			T dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D;
708 			T dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D;
709 			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4;
710 			if (attn4 > 0) {
711 				attn4 *= attn4;
712 				value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4);
713 			}
714 
715 			//Contribution (1,0,1)
716 			T dx5 = dx4;
717 			T dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D;
718 			T dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D;
719 			T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5;
720 			if (attn5 > 0) {
721 				attn5 *= attn5;
722 				value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5);
723 			}
724 
725 			//Contribution (0,1,1)
726 			T dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D;
727 			T dy6 = dy4;
728 			T dz6 = dz5;
729 			T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6;
730 			if (attn6 > 0) {
731 				attn6 *= attn6;
732 				value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6);
733 			}
734 		}
735 
736 		//First extra vertex
737 		T attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0;
738 		if (attn_ext0 > 0)
739 		{
740 			attn_ext0 *= attn_ext0;
741 			value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0);
742 		}
743 
744 		//Second extra vertex
745 		T attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1;
746 		if (attn_ext1 > 0)
747 		{
748 			attn_ext1 *= attn_ext1;
749 			value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
750 		}
751 
752 		return value / NORM_CONSTANT_3D;
753 	}
754 
755 	//4D OpenSimplex (Simplectic) Noise.
756 	public T eval(T x, T y, T z, T w) {
757 
758 		//Place input coordinates on simplectic honeycomb.
759 		T stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D;
760 		T xs = x + stretchOffset;
761 		T ys = y + stretchOffset;
762 		T zs = z + stretchOffset;
763 		T ws = w + stretchOffset;
764 
765 		//Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
766 		int xsb = fastFloor(xs);
767 		int ysb = fastFloor(ys);
768 		int zsb = fastFloor(zs);
769 		int wsb = fastFloor(ws);
770 
771 		//Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
772 		T squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D;
773 		T xb = xsb + squishOffset;
774 		T yb = ysb + squishOffset;
775 		T zb = zsb + squishOffset;
776 		T wb = wsb + squishOffset;
777 
778 		//Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
779 		T xins = xs - xsb;
780 		T yins = ys - ysb;
781 		T zins = zs - zsb;
782 		T wins = ws - wsb;
783 
784 		//Sum those together to get a value that determines which region we're in.
785 		T inSum = xins + yins + zins + wins;
786 
787 		//Positions relative to origin point.
788 		T dx0 = x - xb;
789 		T dy0 = y - yb;
790 		T dz0 = z - zb;
791 		T dw0 = w - wb;
792 
793 		//We'll be defining these inside the next block and using them afterwards.
794 		T dx_ext0, dy_ext0, dz_ext0, dw_ext0;
795 		T dx_ext1, dy_ext1, dz_ext1, dw_ext1;
796 		T dx_ext2, dy_ext2, dz_ext2, dw_ext2;
797 		int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0;
798 		int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1;
799 		int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2;
800 
801 		T value = 0;
802 		if (inSum <= 1) { //We're inside the pentachoron (4-Simplex) at (0,0,0,0)
803 
804 			//Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest.
805 			byte aPoint = 0x01;
806 			T aScore = xins;
807 			byte bPoint = 0x02;
808 			T bScore = yins;
809 			if (aScore >= bScore && zins > bScore) {
810 				bScore = zins;
811 				bPoint = 0x04;
812 			} else if (aScore < bScore && zins > aScore) {
813 				aScore = zins;
814 				aPoint = 0x04;
815 			}
816 			if (aScore >= bScore && wins > bScore) {
817 				bScore = wins;
818 				bPoint = 0x08;
819 			} else if (aScore < bScore && wins > aScore) {
820 				aScore = wins;
821 				aPoint = 0x08;
822 			}
823 
824 			//Now we determine the three lattice points not part of the pentachoron that may contribute.
825 			//This depends on the closest two pentachoron vertices, including (0,0,0,0)
826 			T uins = 1 - inSum;
827 			if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices.
828 				byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
829 				if ((c & 0x01) == 0) {
830 					xsv_ext0 = xsb - 1;
831 					xsv_ext1 = xsv_ext2 = xsb;
832 					dx_ext0 = dx0 + 1;
833 					dx_ext1 = dx_ext2 = dx0;
834 				} else {
835 					xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
836 					dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1;
837 				}
838 
839 				if ((c & 0x02) == 0) {
840 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
841 					dy_ext0 = dy_ext1 = dy_ext2 = dy0;
842 					if ((c & 0x01) == 0x01) {
843 						ysv_ext0 -= 1;
844 						dy_ext0 += 1;
845 					} else {
846 						ysv_ext1 -= 1;
847 						dy_ext1 += 1;
848 					}
849 				} else {
850 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
851 					dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1;
852 				}
853 
854 				if ((c & 0x04) == 0) {
855 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
856 					dz_ext0 = dz_ext1 = dz_ext2 = dz0;
857 					if ((c & 0x03) != 0) {
858 						if ((c & 0x03) == 0x03) {
859 							zsv_ext0 -= 1;
860 							dz_ext0 += 1;
861 						} else {
862 							zsv_ext1 -= 1;
863 							dz_ext1 += 1;
864 						}
865 					} else {
866 						zsv_ext2 -= 1;
867 						dz_ext2 += 1;
868 					}
869 				} else {
870 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
871 					dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1;
872 				}
873 
874 				if ((c & 0x08) == 0) {
875 					wsv_ext0 = wsv_ext1 = wsb;
876 					wsv_ext2 = wsb - 1;
877 					dw_ext0 = dw_ext1 = dw0;
878 					dw_ext2 = dw0 + 1;
879 				} else {
880 					wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
881 					dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1;
882 				}
883 			} else { //(0,0,0,0) is not one of the closest two pentachoron vertices.
884 				byte c = cast(byte)(aPoint | bPoint); //Our three extra vertices are determined by the closest two.
885 
886 				if ((c & 0x01) == 0) {
887 					xsv_ext0 = xsv_ext2 = xsb;
888 					xsv_ext1 = xsb - 1;
889 					dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D;
890 					dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D;
891 					dx_ext2 = dx0 - SQUISH_CONSTANT_4D;
892 				} else {
893 					xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
894 					dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
895 					dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D;
896 				}
897 
898 				if ((c & 0x02) == 0) {
899 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
900 					dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D;
901 					dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D;
902 					if ((c & 0x01) == 0x01) {
903 						ysv_ext1 -= 1;
904 						dy_ext1 += 1;
905 					} else {
906 						ysv_ext2 -= 1;
907 						dy_ext2 += 1;
908 					}
909 				} else {
910 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
911 					dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
912 					dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D;
913 				}
914 
915 				if ((c & 0x04) == 0) {
916 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
917 					dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D;
918 					dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D;
919 					if ((c & 0x03) == 0x03) {
920 						zsv_ext1 -= 1;
921 						dz_ext1 += 1;
922 					} else {
923 						zsv_ext2 -= 1;
924 						dz_ext2 += 1;
925 					}
926 				} else {
927 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
928 					dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
929 					dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D;
930 				}
931 
932 				if ((c & 0x08) == 0) {
933 					wsv_ext0 = wsv_ext1 = wsb;
934 					wsv_ext2 = wsb - 1;
935 					dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D;
936 					dw_ext1 = dw0 - SQUISH_CONSTANT_4D;
937 					dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D;
938 				} else {
939 					wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
940 					dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
941 					dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D;
942 				}
943 			}
944 
945 			//Contribution (0,0,0,0)
946 			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
947 			if (attn0 > 0) {
948 				attn0 *= attn0;
949 				value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0);
950 			}
951 
952 			//Contribution (1,0,0,0)
953 			T dx1 = dx0 - 1 - SQUISH_CONSTANT_4D;
954 			T dy1 = dy0 - 0 - SQUISH_CONSTANT_4D;
955 			T dz1 = dz0 - 0 - SQUISH_CONSTANT_4D;
956 			T dw1 = dw0 - 0 - SQUISH_CONSTANT_4D;
957 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
958 			if (attn1 > 0) {
959 				attn1 *= attn1;
960 				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1);
961 			}
962 
963 			//Contribution (0,1,0,0)
964 			T dx2 = dx0 - 0 - SQUISH_CONSTANT_4D;
965 			T dy2 = dy0 - 1 - SQUISH_CONSTANT_4D;
966 			T dz2 = dz1;
967 			T dw2 = dw1;
968 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
969 			if (attn2 > 0) {
970 				attn2 *= attn2;
971 				value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2);
972 			}
973 
974 			//Contribution (0,0,1,0)
975 			T dx3 = dx2;
976 			T dy3 = dy1;
977 			T dz3 = dz0 - 1 - SQUISH_CONSTANT_4D;
978 			T dw3 = dw1;
979 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
980 			if (attn3 > 0) {
981 				attn3 *= attn3;
982 				value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3);
983 			}
984 
985 			//Contribution (0,0,0,1)
986 			T dx4 = dx2;
987 			T dy4 = dy1;
988 			T dz4 = dz1;
989 			T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
990 			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
991 			if (attn4 > 0) {
992 				attn4 *= attn4;
993 				value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4);
994 			}
995 		} else if (inSum >= 3) { //We're inside the pentachoron (4-Simplex) at (1,1,1,1)
996 			//Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest.
997 			byte aPoint = 0x0E;
998 			T aScore = xins;
999 			byte bPoint = 0x0D;
1000 			T bScore = yins;
1001 			if (aScore <= bScore && zins < bScore) {
1002 				bScore = zins;
1003 				bPoint = 0x0B;
1004 			} else if (aScore > bScore && zins < aScore) {
1005 				aScore = zins;
1006 				aPoint = 0x0B;
1007 			}
1008 			if (aScore <= bScore && wins < bScore) {
1009 				bScore = wins;
1010 				bPoint = 0x07;
1011 			} else if (aScore > bScore && wins < aScore) {
1012 				aScore = wins;
1013 				aPoint = 0x07;
1014 			}
1015 
1016 			//Now we determine the three lattice points not part of the pentachoron that may contribute.
1017 			//This depends on the closest two pentachoron vertices, including (0,0,0,0)
1018 			T uins = 4 - inSum;
1019 			if (uins < aScore || uins < bScore) { //(1,1,1,1) is one of the closest two pentachoron vertices.
1020 				byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
1021 
1022 				if ((c & 0x01) != 0) {
1023 					xsv_ext0 = xsb + 2;
1024 					xsv_ext1 = xsv_ext2 = xsb + 1;
1025 					dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D;
1026 					dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
1027 				} else {
1028 					xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
1029 					dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D;
1030 				}
1031 
1032 				if ((c & 0x02) != 0) {
1033 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
1034 					dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
1035 					if ((c & 0x01) != 0) {
1036 						ysv_ext1 += 1;
1037 						dy_ext1 -= 1;
1038 					} else {
1039 						ysv_ext0 += 1;
1040 						dy_ext0 -= 1;
1041 					}
1042 				} else {
1043 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
1044 					dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D;
1045 				}
1046 
1047 				if ((c & 0x04) != 0) {
1048 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
1049 					dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
1050 					if ((c & 0x03) != 0x03) {
1051 						if ((c & 0x03) == 0) {
1052 							zsv_ext0 += 1;
1053 							dz_ext0 -= 1;
1054 						} else {
1055 							zsv_ext1 += 1;
1056 							dz_ext1 -= 1;
1057 						}
1058 					} else {
1059 						zsv_ext2 += 1;
1060 						dz_ext2 -= 1;
1061 					}
1062 				} else {
1063 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
1064 					dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D;
1065 				}
1066 
1067 				if ((c & 0x08) != 0) {
1068 					wsv_ext0 = wsv_ext1 = wsb + 1;
1069 					wsv_ext2 = wsb + 2;
1070 					dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
1071 					dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D;
1072 				} else {
1073 					wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
1074 					dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D;
1075 				}
1076 			} else { //(1,1,1,1) is not one of the closest two pentachoron vertices.
1077 				byte c = cast(byte)(aPoint & bPoint); //Our three extra vertices are determined by the closest two.
1078 
1079 				if ((c & 0x01) != 0) {
1080 					xsv_ext0 = xsv_ext2 = xsb + 1;
1081 					xsv_ext1 = xsb + 2;
1082 					dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1083 					dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
1084 					dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1085 				} else {
1086 					xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
1087 					dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D;
1088 					dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D;
1089 				}
1090 
1091 				if ((c & 0x02) != 0) {
1092 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
1093 					dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1094 					dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1095 					if ((c & 0x01) != 0) {
1096 						ysv_ext2 += 1;
1097 						dy_ext2 -= 1;
1098 					} else {
1099 						ysv_ext1 += 1;
1100 						dy_ext1 -= 1;
1101 					}
1102 				} else {
1103 					ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
1104 					dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D;
1105 					dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D;
1106 				}
1107 
1108 				if ((c & 0x04) != 0) {
1109 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
1110 					dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1111 					dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1112 					if ((c & 0x03) != 0) {
1113 						zsv_ext2 += 1;
1114 						dz_ext2 -= 1;
1115 					} else {
1116 						zsv_ext1 += 1;
1117 						dz_ext1 -= 1;
1118 					}
1119 				} else {
1120 					zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
1121 					dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D;
1122 					dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D;
1123 				}
1124 
1125 				if ((c & 0x08) != 0) {
1126 					wsv_ext0 = wsv_ext1 = wsb + 1;
1127 					wsv_ext2 = wsb + 2;
1128 					dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1129 					dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1130 					dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
1131 				} else {
1132 					wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
1133 					dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D;
1134 					dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D;
1135 				}
1136 			}
1137 
1138 			//Contribution (1,1,1,0)
1139 			T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1140 			T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1141 			T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1142 			T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
1143 			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
1144 			if (attn4 > 0) {
1145 				attn4 *= attn4;
1146 				value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
1147 			}
1148 
1149 			//Contribution (1,1,0,1)
1150 			T dx3 = dx4;
1151 			T dy3 = dy4;
1152 			T dz3 = dz0 - 3 * SQUISH_CONSTANT_4D;
1153 			T dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1154 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
1155 			if (attn3 > 0) {
1156 				attn3 *= attn3;
1157 				value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3);
1158 			}
1159 
1160 			//Contribution (1,0,1,1)
1161 			T dx2 = dx4;
1162 			T dy2 = dy0 - 3 * SQUISH_CONSTANT_4D;
1163 			T dz2 = dz4;
1164 			T dw2 = dw3;
1165 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
1166 			if (attn2 > 0) {
1167 				attn2 *= attn2;
1168 				value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
1169 			}
1170 
1171 			//Contribution (0,1,1,1)
1172 			T dx1 = dx0 - 3 * SQUISH_CONSTANT_4D;
1173 			T dz1 = dz4;
1174 			T dy1 = dy4;
1175 			T dw1 = dw3;
1176 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
1177 			if (attn1 > 0) {
1178 				attn1 *= attn1;
1179 				value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
1180 			}
1181 
1182 			//Contribution (1,1,1,1)
1183 			dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
1184 			dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
1185 			dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
1186 			dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
1187 			T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0;
1188 			if (attn0 > 0) {
1189 				attn0 *= attn0;
1190 				value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0);
1191 			}
1192 		} else if (inSum <= 2) { //We're inside the first dispentachoron (Rectified 4-Simplex)
1193 			T aScore;
1194 			byte aPoint;
1195 			bool aIsBiggerSide = true;
1196 			T bScore;
1197 			byte bPoint;
1198 			bool bIsBiggerSide = true;
1199 
1200 			//Decide between (1,1,0,0) and (0,0,1,1)
1201 			if (xins + yins > zins + wins) {
1202 				aScore = xins + yins;
1203 				aPoint = 0x03;
1204 			} else {
1205 				aScore = zins + wins;
1206 				aPoint = 0x0C;
1207 			}
1208 
1209 			//Decide between (1,0,1,0) and (0,1,0,1)
1210 			if (xins + zins > yins + wins) {
1211 				bScore = xins + zins;
1212 				bPoint = 0x05;
1213 			} else {
1214 				bScore = yins + wins;
1215 				bPoint = 0x0A;
1216 			}
1217 
1218 			//Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer.
1219 			if (xins + wins > yins + zins) {
1220 				T score = xins + wins;
1221 				if (aScore >= bScore && score > bScore) {
1222 					bScore = score;
1223 					bPoint = 0x09;
1224 				} else if (aScore < bScore && score > aScore) {
1225 					aScore = score;
1226 					aPoint = 0x09;
1227 				}
1228 			} else {
1229 				T score = yins + zins;
1230 				if (aScore >= bScore && score > bScore) {
1231 					bScore = score;
1232 					bPoint = 0x06;
1233 				} else if (aScore < bScore && score > aScore) {
1234 					aScore = score;
1235 					aPoint = 0x06;
1236 				}
1237 			}
1238 
1239 			//Decide if (1,0,0,0) is closer.
1240 			T p1 = 2 - inSum + xins;
1241 			if (aScore >= bScore && p1 > bScore) {
1242 				bScore = p1;
1243 				bPoint = 0x01;
1244 				bIsBiggerSide = false;
1245 			} else if (aScore < bScore && p1 > aScore) {
1246 				aScore = p1;
1247 				aPoint = 0x01;
1248 				aIsBiggerSide = false;
1249 			}
1250 
1251 			//Decide if (0,1,0,0) is closer.
1252 			T p2 = 2 - inSum + yins;
1253 			if (aScore >= bScore && p2 > bScore) {
1254 				bScore = p2;
1255 				bPoint = 0x02;
1256 				bIsBiggerSide = false;
1257 			} else if (aScore < bScore && p2 > aScore) {
1258 				aScore = p2;
1259 				aPoint = 0x02;
1260 				aIsBiggerSide = false;
1261 			}
1262 
1263 			//Decide if (0,0,1,0) is closer.
1264 			T p3 = 2 - inSum + zins;
1265 			if (aScore >= bScore && p3 > bScore) {
1266 				bScore = p3;
1267 				bPoint = 0x04;
1268 				bIsBiggerSide = false;
1269 			} else if (aScore < bScore && p3 > aScore) {
1270 				aScore = p3;
1271 				aPoint = 0x04;
1272 				aIsBiggerSide = false;
1273 			}
1274 
1275 			//Decide if (0,0,0,1) is closer.
1276 			T p4 = 2 - inSum + wins;
1277 			if (aScore >= bScore && p4 > bScore) {
1278 				bScore = p4;
1279 				bPoint = 0x08;
1280 				bIsBiggerSide = false;
1281 			} else if (aScore < bScore && p4 > aScore) {
1282 				aScore = p4;
1283 				aPoint = 0x08;
1284 				aIsBiggerSide = false;
1285 			}
1286 
1287 			//Where each of the two closest points are determines how the extra three vertices are calculated.
1288 			if (aIsBiggerSide == bIsBiggerSide) {
1289 				if (aIsBiggerSide) { //Both closest points on the bigger side
1290 					byte c1 = cast(byte)(aPoint | bPoint);
1291 					byte c2 = cast(byte)(aPoint & bPoint);
1292 					if ((c1 & 0x01) == 0) {
1293 						xsv_ext0 = xsb;
1294 						xsv_ext1 = xsb - 1;
1295 						dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D;
1296 						dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D;
1297 					} else {
1298 						xsv_ext0 = xsv_ext1 = xsb + 1;
1299 						dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1300 						dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1301 					}
1302 
1303 					if ((c1 & 0x02) == 0) {
1304 						ysv_ext0 = ysb;
1305 						ysv_ext1 = ysb - 1;
1306 						dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D;
1307 						dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D;
1308 					} else {
1309 						ysv_ext0 = ysv_ext1 = ysb + 1;
1310 						dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1311 						dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1312 					}
1313 
1314 					if ((c1 & 0x04) == 0) {
1315 						zsv_ext0 = zsb;
1316 						zsv_ext1 = zsb - 1;
1317 						dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D;
1318 						dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D;
1319 					} else {
1320 						zsv_ext0 = zsv_ext1 = zsb + 1;
1321 						dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1322 						dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1323 					}
1324 
1325 					if ((c1 & 0x08) == 0) {
1326 						wsv_ext0 = wsb;
1327 						wsv_ext1 = wsb - 1;
1328 						dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D;
1329 						dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D;
1330 					} else {
1331 						wsv_ext0 = wsv_ext1 = wsb + 1;
1332 						dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1333 						dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1334 					}
1335 
1336 					//One combination is a permutation of (0,0,0,2) based on c2
1337 					xsv_ext2 = xsb;
1338 					ysv_ext2 = ysb;
1339 					zsv_ext2 = zsb;
1340 					wsv_ext2 = wsb;
1341 					dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D;
1342 					dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D;
1343 					dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D;
1344 					dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D;
1345 					if ((c2 & 0x01) != 0) {
1346 						xsv_ext2 += 2;
1347 						dx_ext2 -= 2;
1348 					} else if ((c2 & 0x02) != 0) {
1349 						ysv_ext2 += 2;
1350 						dy_ext2 -= 2;
1351 					} else if ((c2 & 0x04) != 0) {
1352 						zsv_ext2 += 2;
1353 						dz_ext2 -= 2;
1354 					} else {
1355 						wsv_ext2 += 2;
1356 						dw_ext2 -= 2;
1357 					}
1358 
1359 				} else { //Both closest points on the smaller side
1360 					//One of the two extra points is (0,0,0,0)
1361 					xsv_ext2 = xsb;
1362 					ysv_ext2 = ysb;
1363 					zsv_ext2 = zsb;
1364 					wsv_ext2 = wsb;
1365 					dx_ext2 = dx0;
1366 					dy_ext2 = dy0;
1367 					dz_ext2 = dz0;
1368 					dw_ext2 = dw0;
1369 
1370 					//Other two points are based on the omitted axes.
1371 					byte c = cast(byte)(aPoint | bPoint);
1372 
1373 					if ((c & 0x01) == 0) {
1374 						xsv_ext0 = xsb - 1;
1375 						xsv_ext1 = xsb;
1376 						dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D;
1377 						dx_ext1 = dx0 - SQUISH_CONSTANT_4D;
1378 					} else {
1379 						xsv_ext0 = xsv_ext1 = xsb + 1;
1380 						dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D;
1381 					}
1382 
1383 					if ((c & 0x02) == 0) {
1384 						ysv_ext0 = ysv_ext1 = ysb;
1385 						dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D;
1386 						if ((c & 0x01) == 0x01)
1387 						{
1388 							ysv_ext0 -= 1;
1389 							dy_ext0 += 1;
1390 						} else {
1391 							ysv_ext1 -= 1;
1392 							dy_ext1 += 1;
1393 						}
1394 					} else {
1395 						ysv_ext0 = ysv_ext1 = ysb + 1;
1396 						dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D;
1397 					}
1398 
1399 					if ((c & 0x04) == 0) {
1400 						zsv_ext0 = zsv_ext1 = zsb;
1401 						dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D;
1402 						if ((c & 0x03) == 0x03)
1403 						{
1404 							zsv_ext0 -= 1;
1405 							dz_ext0 += 1;
1406 						} else {
1407 							zsv_ext1 -= 1;
1408 							dz_ext1 += 1;
1409 						}
1410 					} else {
1411 						zsv_ext0 = zsv_ext1 = zsb + 1;
1412 						dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D;
1413 					}
1414 
1415 					if ((c & 0x08) == 0)
1416 					{
1417 						wsv_ext0 = wsb;
1418 						wsv_ext1 = wsb - 1;
1419 						dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
1420 						dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D;
1421 					} else {
1422 						wsv_ext0 = wsv_ext1 = wsb + 1;
1423 						dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D;
1424 					}
1425 
1426 				}
1427 			} else { //One point on each "side"
1428 				byte c1, c2;
1429 				if (aIsBiggerSide) {
1430 					c1 = aPoint;
1431 					c2 = bPoint;
1432 				} else {
1433 					c1 = bPoint;
1434 					c2 = aPoint;
1435 				}
1436 
1437 				//Two contributions are the bigger-sided point with each 0 replaced with -1.
1438 				if ((c1 & 0x01) == 0) {
1439 					xsv_ext0 = xsb - 1;
1440 					xsv_ext1 = xsb;
1441 					dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D;
1442 					dx_ext1 = dx0 - SQUISH_CONSTANT_4D;
1443 				} else {
1444 					xsv_ext0 = xsv_ext1 = xsb + 1;
1445 					dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D;
1446 				}
1447 
1448 				if ((c1 & 0x02) == 0) {
1449 					ysv_ext0 = ysv_ext1 = ysb;
1450 					dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D;
1451 					if ((c1 & 0x01) == 0x01) {
1452 						ysv_ext0 -= 1;
1453 						dy_ext0 += 1;
1454 					} else {
1455 						ysv_ext1 -= 1;
1456 						dy_ext1 += 1;
1457 					}
1458 				} else {
1459 					ysv_ext0 = ysv_ext1 = ysb + 1;
1460 					dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D;
1461 				}
1462 
1463 				if ((c1 & 0x04) == 0) {
1464 					zsv_ext0 = zsv_ext1 = zsb;
1465 					dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D;
1466 					if ((c1 & 0x03) == 0x03) {
1467 						zsv_ext0 -= 1;
1468 						dz_ext0 += 1;
1469 					} else {
1470 						zsv_ext1 -= 1;
1471 						dz_ext1 += 1;
1472 					}
1473 				} else {
1474 					zsv_ext0 = zsv_ext1 = zsb + 1;
1475 					dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D;
1476 				}
1477 
1478 				if ((c1 & 0x08) == 0) {
1479 					wsv_ext0 = wsb;
1480 					wsv_ext1 = wsb - 1;
1481 					dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
1482 					dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D;
1483 				} else {
1484 					wsv_ext0 = wsv_ext1 = wsb + 1;
1485 					dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D;
1486 				}
1487 
1488 				//One contribution is a permutation of (0,0,0,2) based on the smaller-sided point
1489 				xsv_ext2 = xsb;
1490 				ysv_ext2 = ysb;
1491 				zsv_ext2 = zsb;
1492 				wsv_ext2 = wsb;
1493 				dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D;
1494 				dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D;
1495 				dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D;
1496 				dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D;
1497 				if ((c2 & 0x01) != 0) {
1498 					xsv_ext2 += 2;
1499 					dx_ext2 -= 2;
1500 				} else if ((c2 & 0x02) != 0) {
1501 					ysv_ext2 += 2;
1502 					dy_ext2 -= 2;
1503 				} else if ((c2 & 0x04) != 0) {
1504 					zsv_ext2 += 2;
1505 					dz_ext2 -= 2;
1506 				} else {
1507 					wsv_ext2 += 2;
1508 					dw_ext2 -= 2;
1509 				}
1510 			}
1511 
1512 			//Contribution (1,0,0,0)
1513 			T dx1 = dx0 - 1 - SQUISH_CONSTANT_4D;
1514 			T dy1 = dy0 - 0 - SQUISH_CONSTANT_4D;
1515 			T dz1 = dz0 - 0 - SQUISH_CONSTANT_4D;
1516 			T dw1 = dw0 - 0 - SQUISH_CONSTANT_4D;
1517 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
1518 			if (attn1 > 0) {
1519 				attn1 *= attn1;
1520 				value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1);
1521 			}
1522 
1523 			//Contribution (0,1,0,0)
1524 			T dx2 = dx0 - 0 - SQUISH_CONSTANT_4D;
1525 			T dy2 = dy0 - 1 - SQUISH_CONSTANT_4D;
1526 			T dz2 = dz1;
1527 			T dw2 = dw1;
1528 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
1529 			if (attn2 > 0) {
1530 				attn2 *= attn2;
1531 				value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2);
1532 			}
1533 
1534 			//Contribution (0,0,1,0)
1535 			T dx3 = dx2;
1536 			T dy3 = dy1;
1537 			T dz3 = dz0 - 1 - SQUISH_CONSTANT_4D;
1538 			T dw3 = dw1;
1539 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
1540 			if (attn3 > 0) {
1541 				attn3 *= attn3;
1542 				value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3);
1543 			}
1544 
1545 			//Contribution (0,0,0,1)
1546 			T dx4 = dx2;
1547 			T dy4 = dy1;
1548 			T dz4 = dz1;
1549 			T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D;
1550 			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
1551 			if (attn4 > 0) {
1552 				attn4 *= attn4;
1553 				value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4);
1554 			}
1555 
1556 			//Contribution (1,1,0,0)
1557 			T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1558 			T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1559 			T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
1560 			T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
1561 			T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
1562 			if (attn5 > 0) {
1563 				attn5 *= attn5;
1564 				value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
1565 			}
1566 
1567 			//Contribution (1,0,1,0)
1568 			T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1569 			T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
1570 			T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1571 			T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
1572 			T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
1573 			if (attn6 > 0) {
1574 				attn6 *= attn6;
1575 				value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
1576 			}
1577 
1578 			//Contribution (1,0,0,1)
1579 			T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1580 			T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
1581 			T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
1582 			T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1583 			T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
1584 			if (attn7 > 0) {
1585 				attn7 *= attn7;
1586 				value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
1587 			}
1588 
1589 			//Contribution (0,1,1,0)
1590 			T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
1591 			T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1592 			T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1593 			T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
1594 			T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
1595 			if (attn8 > 0) {
1596 				attn8 *= attn8;
1597 				value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
1598 			}
1599 
1600 			//Contribution (0,1,0,1)
1601 			T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
1602 			T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1603 			T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
1604 			T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1605 			T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
1606 			if (attn9 > 0) {
1607 				attn9 *= attn9;
1608 				value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
1609 			}
1610 
1611 			//Contribution (0,0,1,1)
1612 			T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
1613 			T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
1614 			T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1615 			T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1616 			T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
1617 			if (attn10 > 0) {
1618 				attn10 *= attn10;
1619 				value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
1620 			}
1621 		} else { //We're inside the second dispentachoron (Rectified 4-Simplex)
1622 			T aScore;
1623 			byte aPoint;
1624 			bool aIsBiggerSide = true;
1625 			T bScore;
1626 			byte bPoint;
1627 			bool bIsBiggerSide = true;
1628 
1629 			//Decide between (0,0,1,1) and (1,1,0,0)
1630 			if (xins + yins < zins + wins) {
1631 				aScore = xins + yins;
1632 				aPoint = 0x0C;
1633 			} else {
1634 				aScore = zins + wins;
1635 				aPoint = 0x03;
1636 			}
1637 
1638 			//Decide between (0,1,0,1) and (1,0,1,0)
1639 			if (xins + zins < yins + wins) {
1640 				bScore = xins + zins;
1641 				bPoint = 0x0A;
1642 			} else {
1643 				bScore = yins + wins;
1644 				bPoint = 0x05;
1645 			}
1646 
1647 			//Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer.
1648 			if (xins + wins < yins + zins) {
1649 				T score = xins + wins;
1650 				if (aScore <= bScore && score < bScore) {
1651 					bScore = score;
1652 					bPoint = 0x06;
1653 				} else if (aScore > bScore && score < aScore) {
1654 					aScore = score;
1655 					aPoint = 0x06;
1656 				}
1657 			} else {
1658 				T score = yins + zins;
1659 				if (aScore <= bScore && score < bScore) {
1660 					bScore = score;
1661 					bPoint = 0x09;
1662 				} else if (aScore > bScore && score < aScore) {
1663 					aScore = score;
1664 					aPoint = 0x09;
1665 				}
1666 			}
1667 
1668 			//Decide if (0,1,1,1) is closer.
1669 			T p1 = 3 - inSum + xins;
1670 			if (aScore <= bScore && p1 < bScore) {
1671 				bScore = p1;
1672 				bPoint = 0x0E;
1673 				bIsBiggerSide = false;
1674 			} else if (aScore > bScore && p1 < aScore) {
1675 				aScore = p1;
1676 				aPoint = 0x0E;
1677 				aIsBiggerSide = false;
1678 			}
1679 
1680 			//Decide if (1,0,1,1) is closer.
1681 			T p2 = 3 - inSum + yins;
1682 			if (aScore <= bScore && p2 < bScore) {
1683 				bScore = p2;
1684 				bPoint = 0x0D;
1685 				bIsBiggerSide = false;
1686 			} else if (aScore > bScore && p2 < aScore) {
1687 				aScore = p2;
1688 				aPoint = 0x0D;
1689 				aIsBiggerSide = false;
1690 			}
1691 
1692 			//Decide if (1,1,0,1) is closer.
1693 			T p3 = 3 - inSum + zins;
1694 			if (aScore <= bScore && p3 < bScore) {
1695 				bScore = p3;
1696 				bPoint = 0x0B;
1697 				bIsBiggerSide = false;
1698 			} else if (aScore > bScore && p3 < aScore) {
1699 				aScore = p3;
1700 				aPoint = 0x0B;
1701 				aIsBiggerSide = false;
1702 			}
1703 
1704 			//Decide if (1,1,1,0) is closer.
1705 			T p4 = 3 - inSum + wins;
1706 			if (aScore <= bScore && p4 < bScore) {
1707 				bScore = p4;
1708 				bPoint = 0x07;
1709 				bIsBiggerSide = false;
1710 			} else if (aScore > bScore && p4 < aScore) {
1711 				aScore = p4;
1712 				aPoint = 0x07;
1713 				aIsBiggerSide = false;
1714 			}
1715 
1716 			//Where each of the two closest points are determines how the extra three vertices are calculated.
1717 			if (aIsBiggerSide == bIsBiggerSide) {
1718 				if (aIsBiggerSide) { //Both closest points on the bigger side
1719 					byte c1 = cast(byte)(aPoint & bPoint);
1720 					byte c2 = cast(byte)(aPoint | bPoint);
1721 
1722 					//Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1
1723 					xsv_ext0 = xsv_ext1 = xsb;
1724 					ysv_ext0 = ysv_ext1 = ysb;
1725 					zsv_ext0 = zsv_ext1 = zsb;
1726 					wsv_ext0 = wsv_ext1 = wsb;
1727 					dx_ext0 = dx0 - SQUISH_CONSTANT_4D;
1728 					dy_ext0 = dy0 - SQUISH_CONSTANT_4D;
1729 					dz_ext0 = dz0 - SQUISH_CONSTANT_4D;
1730 					dw_ext0 = dw0 - SQUISH_CONSTANT_4D;
1731 					dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D;
1732 					dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D;
1733 					dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D;
1734 					dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D;
1735 					if ((c1 & 0x01) != 0) {
1736 						xsv_ext0 += 1;
1737 						dx_ext0 -= 1;
1738 						xsv_ext1 += 2;
1739 						dx_ext1 -= 2;
1740 					} else if ((c1 & 0x02) != 0) {
1741 						ysv_ext0 += 1;
1742 						dy_ext0 -= 1;
1743 						ysv_ext1 += 2;
1744 						dy_ext1 -= 2;
1745 					} else if ((c1 & 0x04) != 0) {
1746 						zsv_ext0 += 1;
1747 						dz_ext0 -= 1;
1748 						zsv_ext1 += 2;
1749 						dz_ext1 -= 2;
1750 					} else {
1751 						wsv_ext0 += 1;
1752 						dw_ext0 -= 1;
1753 						wsv_ext1 += 2;
1754 						dw_ext1 -= 2;
1755 					}
1756 
1757 					//One contribution is a permutation of (1,1,1,-1) based on c2
1758 					xsv_ext2 = xsb + 1;
1759 					ysv_ext2 = ysb + 1;
1760 					zsv_ext2 = zsb + 1;
1761 					wsv_ext2 = wsb + 1;
1762 					dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1763 					dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1764 					dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1765 					dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1766 					if ((c2 & 0x01) == 0) {
1767 						xsv_ext2 -= 2;
1768 						dx_ext2 += 2;
1769 					} else if ((c2 & 0x02) == 0) {
1770 						ysv_ext2 -= 2;
1771 						dy_ext2 += 2;
1772 					} else if ((c2 & 0x04) == 0) {
1773 						zsv_ext2 -= 2;
1774 						dz_ext2 += 2;
1775 					} else {
1776 						wsv_ext2 -= 2;
1777 						dw_ext2 += 2;
1778 					}
1779 				} else { //Both closest points on the smaller side
1780 					//One of the two extra points is (1,1,1,1)
1781 					xsv_ext2 = xsb + 1;
1782 					ysv_ext2 = ysb + 1;
1783 					zsv_ext2 = zsb + 1;
1784 					wsv_ext2 = wsb + 1;
1785 					dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D;
1786 					dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D;
1787 					dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D;
1788 					dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D;
1789 
1790 					//Other two points are based on the shared axes.
1791 					byte c = cast(byte)(aPoint & bPoint);
1792 
1793 					if ((c & 0x01) != 0) {
1794 						xsv_ext0 = xsb + 2;
1795 						xsv_ext1 = xsb + 1;
1796 						dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
1797 						dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1798 					} else {
1799 						xsv_ext0 = xsv_ext1 = xsb;
1800 						dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D;
1801 					}
1802 
1803 					if ((c & 0x02) != 0) {
1804 						ysv_ext0 = ysv_ext1 = ysb + 1;
1805 						dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1806 						if ((c & 0x01) == 0)
1807 						{
1808 							ysv_ext0 += 1;
1809 							dy_ext0 -= 1;
1810 						} else {
1811 							ysv_ext1 += 1;
1812 							dy_ext1 -= 1;
1813 						}
1814 					} else {
1815 						ysv_ext0 = ysv_ext1 = ysb;
1816 						dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D;
1817 					}
1818 
1819 					if ((c & 0x04) != 0) {
1820 						zsv_ext0 = zsv_ext1 = zsb + 1;
1821 						dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1822 						if ((c & 0x03) == 0)
1823 						{
1824 							zsv_ext0 += 1;
1825 							dz_ext0 -= 1;
1826 						} else {
1827 							zsv_ext1 += 1;
1828 							dz_ext1 -= 1;
1829 						}
1830 					} else {
1831 						zsv_ext0 = zsv_ext1 = zsb;
1832 						dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D;
1833 					}
1834 
1835 					if ((c & 0x08) != 0)
1836 					{
1837 						wsv_ext0 = wsb + 1;
1838 						wsv_ext1 = wsb + 2;
1839 						dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1840 						dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
1841 					} else {
1842 						wsv_ext0 = wsv_ext1 = wsb;
1843 						dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D;
1844 					}
1845 				}
1846 			} else { //One point on each "side"
1847 				byte c1, c2;
1848 				if (aIsBiggerSide) {
1849 					c1 = aPoint;
1850 					c2 = bPoint;
1851 				} else {
1852 					c1 = bPoint;
1853 					c2 = aPoint;
1854 				}
1855 
1856 				//Two contributions are the bigger-sided point with each 1 replaced with 2.
1857 				if ((c1 & 0x01) != 0) {
1858 					xsv_ext0 = xsb + 2;
1859 					xsv_ext1 = xsb + 1;
1860 					dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D;
1861 					dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1862 				} else {
1863 					xsv_ext0 = xsv_ext1 = xsb;
1864 					dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D;
1865 				}
1866 
1867 				if ((c1 & 0x02) != 0) {
1868 					ysv_ext0 = ysv_ext1 = ysb + 1;
1869 					dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1870 					if ((c1 & 0x01) == 0) {
1871 						ysv_ext0 += 1;
1872 						dy_ext0 -= 1;
1873 					} else {
1874 						ysv_ext1 += 1;
1875 						dy_ext1 -= 1;
1876 					}
1877 				} else {
1878 					ysv_ext0 = ysv_ext1 = ysb;
1879 					dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D;
1880 				}
1881 
1882 				if ((c1 & 0x04) != 0) {
1883 					zsv_ext0 = zsv_ext1 = zsb + 1;
1884 					dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1885 					if ((c1 & 0x03) == 0) {
1886 						zsv_ext0 += 1;
1887 						dz_ext0 -= 1;
1888 					} else {
1889 						zsv_ext1 += 1;
1890 						dz_ext1 -= 1;
1891 					}
1892 				} else {
1893 					zsv_ext0 = zsv_ext1 = zsb;
1894 					dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D;
1895 				}
1896 
1897 				if ((c1 & 0x08) != 0) {
1898 					wsv_ext0 = wsb + 1;
1899 					wsv_ext1 = wsb + 2;
1900 					dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1901 					dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D;
1902 				} else {
1903 					wsv_ext0 = wsv_ext1 = wsb;
1904 					dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D;
1905 				}
1906 
1907 				//One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point
1908 				xsv_ext2 = xsb + 1;
1909 				ysv_ext2 = ysb + 1;
1910 				zsv_ext2 = zsb + 1;
1911 				wsv_ext2 = wsb + 1;
1912 				dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1913 				dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1914 				dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1915 				dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
1916 				if ((c2 & 0x01) == 0) {
1917 					xsv_ext2 -= 2;
1918 					dx_ext2 += 2;
1919 				} else if ((c2 & 0x02) == 0) {
1920 					ysv_ext2 -= 2;
1921 					dy_ext2 += 2;
1922 				} else if ((c2 & 0x04) == 0) {
1923 					zsv_ext2 -= 2;
1924 					dz_ext2 += 2;
1925 				} else {
1926 					wsv_ext2 -= 2;
1927 					dw_ext2 += 2;
1928 				}
1929 			}
1930 
1931 			//Contribution (1,1,1,0)
1932 			T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D;
1933 			T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D;
1934 			T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D;
1935 			T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D;
1936 			T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4;
1937 			if (attn4 > 0) {
1938 				attn4 *= attn4;
1939 				value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4);
1940 			}
1941 
1942 			//Contribution (1,1,0,1)
1943 			T dx3 = dx4;
1944 			T dy3 = dy4;
1945 			T dz3 = dz0 - 3 * SQUISH_CONSTANT_4D;
1946 			T dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D;
1947 			T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3;
1948 			if (attn3 > 0) {
1949 				attn3 *= attn3;
1950 				value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3);
1951 			}
1952 
1953 			//Contribution (1,0,1,1)
1954 			T dx2 = dx4;
1955 			T dy2 = dy0 - 3 * SQUISH_CONSTANT_4D;
1956 			T dz2 = dz4;
1957 			T dw2 = dw3;
1958 			T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2;
1959 			if (attn2 > 0) {
1960 				attn2 *= attn2;
1961 				value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
1962 			}
1963 
1964 			//Contribution (0,1,1,1)
1965 			T dx1 = dx0 - 3 * SQUISH_CONSTANT_4D;
1966 			T dz1 = dz4;
1967 			T dy1 = dy4;
1968 			T dw1 = dw3;
1969 			T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1;
1970 			if (attn1 > 0) {
1971 				attn1 *= attn1;
1972 				value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
1973 			}
1974 
1975 			//Contribution (1,1,0,0)
1976 			T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1977 			T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
1978 			T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
1979 			T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
1980 			T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5;
1981 			if (attn5 > 0) {
1982 				attn5 *= attn5;
1983 				value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5);
1984 			}
1985 
1986 			//Contribution (1,0,1,0)
1987 			T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1988 			T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
1989 			T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
1990 			T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
1991 			T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6;
1992 			if (attn6 > 0) {
1993 				attn6 *= attn6;
1994 				value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6);
1995 			}
1996 
1997 			//Contribution (1,0,0,1)
1998 			T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D;
1999 			T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
2000 			T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
2001 			T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
2002 			T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7;
2003 			if (attn7 > 0) {
2004 				attn7 *= attn7;
2005 				value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7);
2006 			}
2007 
2008 			//Contribution (0,1,1,0)
2009 			T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
2010 			T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
2011 			T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
2012 			T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D;
2013 			T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8;
2014 			if (attn8 > 0) {
2015 				attn8 *= attn8;
2016 				value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8);
2017 			}
2018 
2019 			//Contribution (0,1,0,1)
2020 			T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
2021 			T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D;
2022 			T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D;
2023 			T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
2024 			T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9;
2025 			if (attn9 > 0) {
2026 				attn9 *= attn9;
2027 				value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9);
2028 			}
2029 
2030 			//Contribution (0,0,1,1)
2031 			T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D;
2032 			T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D;
2033 			T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D;
2034 			T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D;
2035 			T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10;
2036 			if (attn10 > 0) {
2037 				attn10 *= attn10;
2038 				value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
2039 			}
2040 		}
2041 
2042 		//First extra vertex
2043 		T attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0;
2044 		if (attn_ext0 > 0)
2045 		{
2046 			attn_ext0 *= attn_ext0;
2047 			value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0);
2048 		}
2049 
2050 		//Second extra vertex
2051 		T attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1;
2052 		if (attn_ext1 > 0)
2053 		{
2054 			attn_ext1 *= attn_ext1;
2055 			value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1);
2056 		}
2057 
2058 		//Third extra vertex
2059 		T attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2;
2060 		if (attn_ext2 > 0)
2061 		{
2062 			attn_ext2 *= attn_ext2;
2063 			value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2);
2064 		}
2065 
2066 		return value / NORM_CONSTANT_4D;
2067 	}
2068 
2069 	private T extrapolate(int xsb, int ysb, T dx, T dy)
2070 	{
2071 		int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
2072 		return gradients2D[index] * dx
2073 			+ gradients2D[index + 1] * dy;
2074 	}
2075 
2076 	private T extrapolate(int xsb, int ysb, int zsb, T dx, T dy, T dz)
2077 	{
2078 		int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
2079 		return gradients3D[index] * dx
2080 			+ gradients3D[index + 1] * dy
2081 			+ gradients3D[index + 2] * dz;
2082 	}
2083 
2084 	private T extrapolate(int xsb, int ysb, int zsb, int wsb, T dx, T dy, T dz, T dw)
2085 	{
2086 		int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC;
2087 		return gradients4D[index] * dx
2088 			+ gradients4D[index + 1] * dy
2089 			+ gradients4D[index + 2] * dz
2090 			+ gradients4D[index + 3] * dw;
2091 	}
2092 
2093 	private static int fastFloor(T x) {
2094 		int xi = cast(int)x;
2095 		return x < xi ? xi - 1 : xi;
2096 	}
2097 
2098 	//Gradients for 2D. They approximate the directions to the
2099 	//vertices of an octagon from the center.
2100 	private static immutable byte[] gradients2D = [
2101 		 5,  2,    2,  5,
2102 		-5,  2,   -2,  5,
2103 		 5, -2,    2, -5,
2104 		-5, -2,   -2, -5,
2105 	];
2106 
2107 	//Gradients for 3D. They approximate the directions to the
2108 	//vertices of a rhombicuboctahedron from the center, skewed so
2109 	//that the triangular and square facets can be inscribed inside
2110 	//circles of the same radius.
2111 	private static immutable byte[] gradients3D = [
2112 		-11,  4,  4,     -4,  11,  4,    -4,  4,  11,
2113 		 11,  4,  4,      4,  11,  4,     4,  4,  11,
2114 		-11, -4,  4,     -4, -11,  4,    -4, -4,  11,
2115 		 11, -4,  4,      4, -11,  4,     4, -4,  11,
2116 		-11,  4, -4,     -4,  11, -4,    -4,  4, -11,
2117 		 11,  4, -4,      4,  11, -4,     4,  4, -11,
2118 		-11, -4, -4,     -4, -11, -4,    -4, -4, -11,
2119 		 11, -4, -4,      4, -11, -4,     4, -4, -11,
2120 	];
2121 
2122 	//Gradients for 4D. They approximate the directions to the
2123 	//vertices of a disprismatotesseractihexadecachoron from the center,
2124 	//skewed so that the tetrahedral and cubic facets can be inscribed inside
2125 	//spheres of the same radius.
2126 	private static immutable byte[] gradients4D = [
2127 	     3,  1,  1,  1,      1,  3,  1,  1,      1,  1,  3,  1,      1,  1,  1,  3,
2128 	    -3,  1,  1,  1,     -1,  3,  1,  1,     -1,  1,  3,  1,     -1,  1,  1,  3,
2129 	     3, -1,  1,  1,      1, -3,  1,  1,      1, -1,  3,  1,      1, -1,  1,  3,
2130 	    -3, -1,  1,  1,     -1, -3,  1,  1,     -1, -1,  3,  1,     -1, -1,  1,  3,
2131 	     3,  1, -1,  1,      1,  3, -1,  1,      1,  1, -3,  1,      1,  1, -1,  3,
2132 	    -3,  1, -1,  1,     -1,  3, -1,  1,     -1,  1, -3,  1,     -1,  1, -1,  3,
2133 	     3, -1, -1,  1,      1, -3, -1,  1,      1, -1, -3,  1,      1, -1, -1,  3,
2134 	    -3, -1, -1,  1,     -1, -3, -1,  1,     -1, -1, -3,  1,     -1, -1, -1,  3,
2135 	     3,  1,  1, -1,      1,  3,  1, -1,      1,  1,  3, -1,      1,  1,  1, -3,
2136 	    -3,  1,  1, -1,     -1,  3,  1, -1,     -1,  1,  3, -1,     -1,  1,  1, -3,
2137 	     3, -1,  1, -1,      1, -3,  1, -1,      1, -1,  3, -1,      1, -1,  1, -3,
2138 	    -3, -1,  1, -1,     -1, -3,  1, -1,     -1, -1,  3, -1,     -1, -1,  1, -3,
2139 	     3,  1, -1, -1,      1,  3, -1, -1,      1,  1, -3, -1,      1,  1, -1, -3,
2140 	    -3,  1, -1, -1,     -1,  3, -1, -1,     -1,  1, -3, -1,     -1,  1, -1, -3,
2141 	     3, -1, -1, -1,      1, -3, -1, -1,      1, -1, -3, -1,      1, -1, -1, -3,
2142 	    -3, -1, -1, -1,     -1, -3, -1, -1,     -1, -1, -3, -1,     -1, -1, -1, -3,
2143 	];
2144 }